Some people (especially adults) have trouble
with Spakk'r because they feel silly just trying to read the
clues!
Here is a solution (November 2000) by Cory
and Julia from Harrison Middle School in Yarmouth, ME; for
Mrs.Jagolinzer's Math Think Lab class. This seems to be a pretty
prolific class; another solution follows...

The first graders on Spakk'r are counting. They have four
syllables that represent numbers: Ba,
To, Ku, and
Pa. We figured out that
Ba=1, To=4,
Ku=16, and Pa=64.
The clues gave us excerpts of Spakk'r's number system. We wrote down
the excerpts and found that some of them overlapped. One example is:
batoto, babatoto,
bababatoto, tototo,
batototo. Another clue was
babato, bababato,
toto, batoto,
babatoto.... These clues overlapped on the
number "babato." The two clues put together
have a range from babato, through
batototo. We continued in this fashion until
we had figured out a full range with all of the clues included.
From this we reasoned what the syllables meant. We saw:
batoto, then
babatoto. It went up by one
ba, so we figured that
ba was 1. If ba was
1, and the order from one is
ba,baba,bababa,to
this means that this represents 1,2,3 so the next number is 4. So we
figured that to was 4. You add them like
normal numbers.
1+1+1=Ba+Ba+Ba.
So when you get to 7,bababato, the next
number has to be 8. Since you can't use the same syllable more than
three times in one number, you have to add another syllable to the
sequence.
Toto is 8. You add one
ba, then another
ba, then another
ba, then another to
and so on. If you keep this up until you get to
bababatototo you will find that you get to
15 with only ba's and
to's. Since you can't go any higher, you
need a new syllable. This would be ku. You
can go on and on with the same process until you get to,
bababatototokukuku which is 63. Then you
need another syllable which is pa.
Pa is 64. The highest number in the Spakk'r
number system that you can write is
bababatototokukukupapapa. This equals 265.
The answers to the questions on the clues are:
"How would you say 1â in Spakk'r?"
ba.
"How would you say 50â in Spakk'r?"
babakuku.
"What does batotoku mean?" 25.
"What does babato mean?" 6.
"How do you count in Spakk'r?" You count in Spakk'r like this:
ba is 1, so you go
ba, then baba, then
bababa, etc. But you can only have 3
syllables at a time in the certain number, so 4 would have to be
to. You use baâ to
increase the number by one, toâ to increase
the number by 4, kuâ to increase the number
by 16, and paâ to increase the number by
64.

(November, 2000) Same class of Mainiacs,
this time Sarah and Heather:

We started with the clue in which the first graders are
counting "babato,
bababato, toto,
batoto, babatoto,"
We figured that since in the beginning you just add a
ba to each number in the sequence
ba must be the equivalent of one. We then
noticed that after every three bas, where
there would have been four bas, the first
graders then replaced the basâ with a
to. This concluded that
toâ must be equal to four. We had finished
with all but the question on that clue so we went to another clue to
figure out what ku was. The next clue that
we picked was the one where the first grader were counting
"bababatototo, ku,
baku, babaku,
bababaku, toku," We
observed that after bababatototoâ came
ku. Since
bababatototo was equal to fifteen we decided
that ku was equal to sixteen. With this
information we were able to figure out that
pa would be the equivalent of one plus three
bas, three tos, and three kusâ because in the clues they only use a
number three times, so paâ is 64.
The questions and answers that were asked on the Spakk'r
clues:
Q= How do you count in Spakk'r?
A= The numbers that are represented in the counting are square
roots of four. ex. batotokupa = 89,
ba = 1(4 to the 0),
to = 4(4 to the 1),
ku = 16(4 to the 2), and
pa = 64(4 to the 3).
Q= How would you say 1 in Spakk'r?
A= ba
Q= What does babato mean?
A= 6
Q= What does batotoku mean?
A= 25
Q= How would you say 50 in Spakk'r?
A= babakukuku

Well! What a couple of thorough
explanations! I hope, readers, that you take the time to go through
the whole thing and not just look for the answers. There are even
(very small) mistakes in them  see if you can find them!
and now, just as I was finishing putting
this on the wen, I get email from Emily, Elizabeth, and Sarah in the
same class, with another solution for Spakk'r. I hope you understand
if I don't put yours up right here (it's every bit as wonderful, and
at least one of the mistakes is not there!).
Those prolific eighthgraders at Monroe City Middle School in Monroe City, MO sent me this:

Megan, Ashley, Matthew, Joslynn, and Jennifer, from Monroe
City, Missouri have figured out the SPAKK'R problem. They say it
wasn't as hard as GEAP,but was easier than ZNORLIAN.
The answers are:
What is one? ba
What does babato mean? 6
How would you say 50 in SPAKK'R? babakukuku
What does batotoku mean? 25
ba=1
to=four ba's=4
ku=four to's=16
pa=four ku's=64
teacher: Mrs. Barbara Carson, Monroe City Middle
School

eeps comments: thank you for your solutions!
Again, I don't guarantee that solutions are correct just because I
post them :) But this looks pretty compelling.
In general, I'd love to get solutions with
your reasoning attached. It can be tedious to write it all out, but
even if you told us just a part of it, people who were confused might
be able to follow in your footsteps!
What would be the next number you would need
a new syllable for?

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